Compare and edit underlying structure in hash

I have a hash of complex structure and I want to perform a search and replace. The first hash is like the following:

$VAR1 = {
  abc => { 123 => ["xx", "yy", "zy"], 456 => ["ab", "cd", "ef"] },
  def => { 659 => ["wx", "yg", "kl"], 456 => ["as", "sd", "df"] },
  mno => { 987 => ["lk", "dm", "sd"] },
}

and I want to iteratively search for all '123'/'456' elements, and if a match is found, I need to do a comparison of the sublayer, i.e. of ['ab','cd','ef'] and ['as','sd','df'] and in this case, keep only the one with ['ab','cd','ef']. So the output will be as follows:

$VAR1 = {
  abc => { 123 => ["xx", "yy", "zy"], 456 => ["ab", "cd", "ef"] },
  def => { 659 => ["wx", "yg", "kl"] },
  mno => { 987 => ["lk", "dm", "sd"] },
}

So the deletion is based on the substructure, and not index. How can it be done? Thanks for the help!!

Lets assume that I will declare the values to be kept, i.e. I will keep 456 => ["ab", "cd", "ef"] based on a pre-declared value of ["ab", "cd", "ef"] and delete any other instance of 456 anywhere else. The search has to be for every key. so the code will go through the hash, first taking 123 => ["xx", "yy", "zy"] and compare it against the keys throughout the rest of the hash, if no match is found, do nothing. If a match is found, like in the case of 456 => ["ab", "cd", "ef"], it will compare the two, and as I have said that in case of a match the one with ["ab", "cd", "ef"] would be kept, it will keep 456 => ["ab", "cd", "ef"] and discard any other instances of 456 anywhere else in the hash, i.e. it will delete 456 => ["as", "sd", "df"] in this case.

Here is a solution that uses the smart match operator to perform the array comparison:

Update: as Borodin pointed out, my original code was wrong. This is the fixed version.

Update 2: Changed it to choose the values to keep based on a hash structure.

my $VAR1 = {
  abc => { 123 => ["xx", "yy", "zy"], 456 => ["ab", "cd", "ef"] },
  def => { 659 => ["wx", "yg", "kl"], 456 => ["as", "sd", "df"] },
  mno => { 987 => ["lk", "dm", "sd"] },
};

my %keep_values = (
    '456' => ['ab','cd','ef']
);

foreach my $outer_key (keys %$VAR1)
{
    foreach my $keepers (keys %keep_values)
    {
        if (exists $VAR1->{$outer_key}{$keepers} and 
            #use the smart match operator to compare arrays.
            !(@{$VAR1->{$outer_key}{$keepers}} ~~ @{$keep_values{$keepers}}))
        {
            delete $VAR1->{$outer_key}{$keepers};
        }
    }   
}

For more on the smart match operator, see perlop.